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Block #269,054

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/22/2013, 5:12:31 PM Β· Difficulty 9.9554 Β· 6,527,615 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
4b8843e82da181a6088511f4d6a88f39c36b813b348a0f2488fdbc6e57f8fdf7
View on Chainz β†—

Height

#269,054

Difficulty

9.955366

Transactions

2

Size

1.57 KB

Version

2

Bits

09f492d8

Nonce

36,929

Timestamp

11/22/2013, 5:12:31 PM

Confirmations

6,527,615

Mined by

⛏️ P2SHAN2J8mpkuofUk6ZFsoZuH3oPj1ex44w5tz

Merkle Root

b63323eb12df5c92e82926f0931c81adaedf3e967d726df86962817285078adf
Transactions (2)
Coinbase61d05a2db30c49…824eb833ef6262
1 in β†’ 1 out10.0900 XPM109 B
AN2J8mpk…ex44w5tz
e9e42d0f516dba…ecf1762bfc7a02
9 in β†’ 2 out331.1089 XPM1.38 KB
AdaN5Q7F…E8F4UU4CAWYToJ1s…PP84dTQc
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.611 Γ— 10⁹⁷(98-digit number)
16111620187743463326…46852231057234411519
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin βˆ’ 1
1.611 Γ— 10⁹⁷(98-digit number)
16111620187743463326…46852231057234411519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.222 Γ— 10⁹⁷(98-digit number)
32223240375486926653…93704462114468823039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.444 Γ— 10⁹⁷(98-digit number)
64446480750973853306…87408924228937646079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.288 Γ— 10⁹⁸(99-digit number)
12889296150194770661…74817848457875292159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.577 Γ— 10⁹⁸(99-digit number)
25778592300389541322…49635696915750584319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.155 Γ— 10⁹⁸(99-digit number)
51557184600779082645…99271393831501168639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁹(100-digit number)
10311436920155816529…98542787663002337279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.062 Γ— 10⁹⁹(100-digit number)
20622873840311633058…97085575326004674559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.124 Γ— 10⁹⁹(100-digit number)
41245747680623266116…94171150652009349119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.249 Γ— 10⁹⁹(100-digit number)
82491495361246532232…88342301304018698239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,617,358 XPMΒ·at block #6,796,668 Β· updates every 60s
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